Related papers: Algorithms and data structures for matrix-free fin…
Given an array $\mathcal{A}$ of $n$ elements and a value $2 \leq k \leq n$, a frequent item or $k$-majority element is an element occurring in $\mathcal{A}$ more than $n/k$ times. The $k$-majority problem requires finding all of the…
The sparse matrix-vector (SpMV) multiplication is an important computational kernel, but it is notoriously difficult to execute efficiently. This paper investigates algorithm performance for unstructured sparse matrices, which are more…
All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and…
Sparse matrix-vector and matrix-matrix multiplication (SpMV and SpMM) are fundamental in both conventional (graph analytics, scientific computing) and emerging (sparse DNN, GNN) domains. Workload-balancing and parallel-reduction are…
This work evaluates the impact of sparse matrix reordering on the performance of sparse matrix-vector multiplication across different multicore CPU platforms. Reordering can significantly enhance performance by optimizing the non-zero…
Modern GPGPUs provide massive arithmetic throughput, yet many scientific kernels remain limited by memory bandwidth. In particular, repeatedly loading precomputed auxiliary data wastes abundant compute resources while stressing the memory…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
We present a family of spacetree-based multigrid realizations using the tree's multiscale nature to derive coarse grids. They align with matrix-free geometric multigrid solvers as they never assemble the system matrices which is cumbersome…
This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…
We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…
Achieving a substantial part of peak performance on todays and future high-performance computing systems is a major challenge for simulation codes. In this paper we address this question in the context of the numerical solution of partial…
Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems…
Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have…
Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and…